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Question: Answered & Verified by Expert
The value of $\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x$ depends on which of the following? $\quad\mathrm{}$
MathematicsDefinite IntegrationNDANDA 2008 (Phase 2)
Options:
  • A Values of $x$ only
  • B Values of each of $a, b$ and $c$
  • C Value of $c$ only
  • D Value of $b$ only
Solution:
1285 Upvotes Verified Answer
The correct answer is: Value of $c$ only
$\begin{aligned} & \int_{-2}^{2}\left(a x^{3}+b x+c\right) d x \\ &=\left[\frac{a x^{4}}{4}+\frac{b x^{2}}{2}+\frac{c x}{1}\right]_{-2}^{2} \\ &=\left[\frac{a(16)}{4}+\frac{b(4)}{2}+2 c\right]-\left[\frac{a(16)}{4}+\frac{b(4)}{2}-2 c\right]=4 c \end{aligned}$
So, the value of given integral depends on the value of $c$ only

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